DiscreteMath`Combinatorica` extends Mathematica by over 230 functions in combinatorics and graph theory. It includes functions for constructing graphs and other combinatorial objects, computing invariants of these objects, and finally displaying them. The documentation provided here covers only a subset of these functions. Combinatorica is best described in Steven Skiena's book:

Implementing Discrete Mathematics: Combinatorics and Graph Theory in Mathematica, Advanced Book Division, Addison-Wesley, Redwood City CA, June 1990. ISBN number 0-201-50943-1. Japanese translation published by Toppan, Tokyo, July 1992. This book can be ordered on-line.

To load the package:

Permutations and Combinations
Partitions, Compositions, and Young Tableaux
Representing Graphs
Generating Graphs
Properties of Graphs
Algorithmic Graph Theory

Note: For further information about Combinatorica, and to be kept informed about new releases, you may contact the author electronically at The latest release of the package, data bases of interesting graphs, and additional files which may be of interest are available by anonymous FTP from

Animations produced using Combinatorica are also available.